ConstantVelocity4
3D• ConstantVelocity4[cnum, axis1, axis2, C] models a constant velocity joint.
• The origin of axis1 is constrained to be coincident with the origin of axis2, and the relative spin of the two axes is constrained to be equal. The relative spin of the axes is the angle between the reference directions of each axis, and the cross product of the two axes.
• ConstantVelocity4[cnum, axis1, {alpha, guess}, axis2, C] models a constant velocity joint with a symbol alpha used to track the relative spin of axis1.
• ConstantVelocity4 constrains four degrees of freedom. • ConstantVelocity4[cnum, axis1, {alpha, guess}, axis2, ratio, C] causes the relative spin of axis2 to be ratio multiplied by the spin of axis1. This form, with the extra symbol alpha, must be used to have a spin ratio other than 1.
• The constant C, which sets the initial relative spin, is equal to the relative spin of axis2 when the spin of axis1 is zero.
• Without the extra symbol, ConstantVelocity4 generates four constraint equations. In this case the first three equations constrain the origins of the two axes to be coincident, and the fourth equation relates the relative spins of the two parts of the constant velocity joint.
• If the extra symbol form is used, ConstantVelocity4 generates five constraint equations and introduces one new variable, hence constraining four degrees of freedom. In this case the first three equations constrain the origins of the two axes to be coincident, and the fourth and fifth equations relate the relative spin of the two parts of the constant velocity joint to the value of the variable alpha.
• If the form with the extra symbol alpha is used, the constraint becomes singular when the two axes become parallel; use RelativeAngle1 or a gear constraint.
• See also: OrthoRevolute4, SetConstraints, Spherical3, SysCon.
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